Based on the product type expansion model, this paper unifies intellectual property protection, technological gaps, and technological catch-up in a general equilibrium analysis framework to study the dynamic impact mechanism between the intellectual property protection of the developing country and the technological progress of the country. Studies shows that the technological catch-up effect produced by independent innovation and technological imitation will dynamically change with the frontier technology gap, resulting in the impact of intellectual property protection on technological catch-up. This "threshold effect" reasonably explains the paradox that intellectual property protection promotes and inhibits technological progress at the same time at the national level, and the paradox of the inconsistency of intellectual property protection policies in developed countries in different historical periods, and the country's basic innovation and transformation capabilities absorptive capacity with national technology introduction will significantly affect the threshold. Numerical simulations show that a constant low level of intellectual property protection can cause technology-developing countries to fall into the "technology catch-up trap", which helps explain the stagnation of technology in countries such as Brazil and the Philippines since 1980. As the technology gap goes from far to near, it is the best dynamic technology catch-up strategy to gradually loosen and then gradually tighten the IP protection policy, which will help the developing countries get rid of the "technology catch-up trap" and complete the technology catch-up process. Using transnational panel data, a threshold model was used to verify the conclusion that there is a threshold effect. The empirical results are not affected by endogenous problems and different measures of core indicators. This research will help China formulate the best dynamic intellectual property protection policies, promote independent innovation, and promote high-quality economic development.